I don't know about other hosting companies, when we 'Fully Manage' a cloud VPS/VM Instance it includes everything, we setup the server software and configure for speed and reliability, including cPanel settings, internal server configs for php-fpm, etc., etc., plus we will setup high performance web stacks like Apache/Nginx and provide backups automatically of all cPanel accounts on the server.
Many companies will say they 'manage' your server, yet they only will install OS and cPanel, leaving the settings to you for server configuration, or they will install scripts etc, at your request... not before, thus you are directing them to do what you need on your server, but do you know what you need?
I see so many companies doing this, it really is quite annoying for clients to wade through all the misrepresented offers that are out there for comparisons...
Managed hosting is for people who do not know how to setup a server, or don't want to know how to setup and run a server, they just want their sites to run on a server that is properly setup and backed up, etc., hands off, with the support team of the host providing the server management 100%. They just want things to work, be fast and reliable, etc.
Unmanaged hosting would be for someone who is comfortable setting up their own servers, installing the OS, configuring the OS, installing cPanel, Apache/Nginx or other web server configurations, they should understand database setup and configuration, along with security of server, etc., installing 3rd party scripts and services as needed to properly support their web hosting environment.
In short, someone who has unmanaged server better know how to fix it or set it up.